Triangular arbitrage across crypto pairs

Question

An exchange shows three prices (ignore fees and spreads for now):

BTC/USD $= 40{,}000$ (dollars per bitcoin)
ETH/USD $= 2{,}000$ (dollars per ether)
ETH/BTC $= 0.045$ (bitcoin per ether)

Is there an arbitrage? If so, give the exact trades and the profit per $360,000 of capital.

Accepted Answer

The no-arbitrage cross is 	ext{ETH/BTC}{	ext{implied}} = \frac{	ext{ETH/USD}}{	ext{BTC/USD}} = \frac{2{,}000}{40{,}000} = 0.05 	ext{ BTC per ETH}. The market quotes only 0.045, so ether is too cheap in bitcoin terms. Buy ETH with BTC at the cheap cross, then unwind through dollars. Starting with \360{,}000: 1. Buy BTC with USD at 40{,}000: receive 	frac{360{,}000}{40{,}000} = 9 BTC. 2. Buy ETH with BTC at 0.045 BTC per ETH: receive 	frac{9}{0.045} = 200 ETH. 3. Sell ETH for USD at 2{,}000: receive 200 	imes 2{,}000 = \400{,}000. Riskless profit: \40{,}000, about 11.1\%, executed toget…

Triangular arbitrage across crypto pairs

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